Question: $f(t) = 5t+2(g(t))$ $g(t) = 2t^{3}-7t^{2}+2t$ $ f(g(0)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(0)$ . Then we'll know what to plug into the outer function. $g(0) = 2(0^{3})-7(0^{2})+(2)(0)$ $g(0) = 0$ Now we know that $g(0) = 0$ . Let's solve for $f(g(0))$ , which is $f(0)$ $f(0) = (5)(0)+2(g(0))$ To solve for the value of $f$ , we need to solve for the value of $g(0)$ $g(0) = 2(0^{3})-7(0^{2})+(2)(0)$ $g(0) = 0$ That means $f(0) = (5)(0)+(2)(0)$ $f(0) = 0$